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In this presentation about shape optimization by the level set method, p.2, the following definition is given:

Find the most rigid structure $\omega$, of prescribed volume, contained into a given domain $\Omega$, when given external forces are applied.

$$\inf_{\omega \subset \Omega, |\omega|=V} J(\omega)$$

In the above definition, what's the meaning of $$|\omega|=V$$?

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mavavilj
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1 Answers1

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(Promoting my comment to an answer) In this context, $|\omega|=V$ means the volume of $\omega$ is $V$.

Gerry Myerson
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  • Is this some typical property of structures? I.e. is absolute value defined for structures such as $\omega$ and then it means its volume? – mavavilj Aug 17 '16 at 07:03
  • I wouldn't call it an absolute value. There are only so many symbols available, some of them have to be used for more than one concept. So the symbol for absolute value is used more generally for the size of an object. For example, if $S$ is a set, an author might use $|S|$ for the number of elements of $S$. If $A$ is a matrix, an author might use $|A|$ for the determinant of $A$. – Gerry Myerson Aug 17 '16 at 07:08